THE Hf-W ISOTOPIC SYSTEM AND THE ORIGIN OF THE EARTH AND MOON

Author: Stein B. Jacobsen

Background concepts presented by

Adam Ward

Bohdan Nedilko

February 3rd, 2009 UBC EOS 453

Question:

Can Hf-W system be used as a chronometer for the Earth formation and core differentiation?

1. Planet-building and core formation process

2. Radiometric dating using Hf-W system

3. Chondritic meteorites

4. Two-stage Hf-W fractination model

5. Continuous Hf-W core formation model

6. W isotope model constraints from Moon, Mars, Vesta and meteorites

TOPICS

1. Planet-building and core formation process

Solar nebula, a cloud of gas and dust left over from the Sun's formation

“The Earth’s last collision”

Planetary embryos

Chemical complexities: Rate of accretion vs. Rate of nebular cooling

A) RACCR > RCOOL

● Refractories (e.g. W ) accrete first, and● Planets start with partially formed iron cores

B) RACCR < RCOOL

● Planetary matter is well mixed

Source of unstable radioactive elements?129I T1/2 = 17 Myr 26AL T1/2 = 0.72 Myr 182Hf T1/2 = 9 Myr

The Christmas Tree Cluster

Hafnium●Hafnium has many isotopes most of which are stable●The most common is Hf-180 making up 35% of the natural abundance●Hf-182 beta decays to W-182 with a half life of 9 Myr●Lithophilic

Tungsten●W-183 and W-182 have a natural abundance of 14.3% and 26.5% respectively●Both are stable and W-182 is the daughter product of the Hf-182 decay.●Siderophilic

Beta Decayn0 → p+ + e− + νe

●A neutron decays to a proton, electron and an anti-neutrino.●The number of nucleons is unchanged, but the atomic number increases by 1

Hf-182 W-182Ta-182

The Hf-W System

Beta Minus Beta Minus144 days9 Myr

Hf182 t = Hf 0182 e− t

How Does Geochronometry Work?●As minerals form from a resevoir, they have different amounts of parent isotopes, but the same amount of daughter isotopes.●As time moves forward the parent decays and the concentrations shift .

Parent

Daughter

Parent

Daughter

●After a sufficient number of half lives decay stops and the concentrations become fixed.●It is important that we have stable isotopes of both the parent and daughter product.

W182

W183 T

= W182

W183 0

Hf182

W183 0

1−e− t

Present Amount

Original Amount

Contribution from Decay

W182

W183 T

= W182

W183 0

Hf182

W183 T

e t−1

W182

W183 T

= W182

W183 0

Hf180

W183 T

Hf182

Hf180 T

e t−1

W182

W183 T

= W182

W183 0

Hf180

W183 T

Hf182

Hf180 0

1−e− t

W182

W183 T

= W182

W183 0

Hf180

W183 T

Hf182

Hf180 0

Measure stable isotope concentrations, at the present time TDerive past values of parent and daughter isotopes from these

W182

W183 T

= W182

W183 0

Hf180

W183 T

Hf182

Hf180 0

Slope

Intercept

Planetary differentiationPlanetary differentiation

CHondritic Unfractionated Reservoir (CHUR)

Bulk Silicate Earth (BSE)

Frames of reference

Meteorites● Chondrites

– Stony meteorites with “chondrules” (Gr. “seed”)– Building blocks of the planetary system

● Achondrites– Stony meteorites w/o “chondrules”

● Stone Irons– Resemble where the Earth core meets the mantle

● Irons– Resemble the outer core of the Earth

Differentiation

Iron meteorites

IIAB IVAB

mm

Chondrites

Chondrules

A) Solidification age

B) Formation age

Many ancient meteorites have S.A. = F.A.

The age of solar system ~4.566 Gy

Ages

Two-stage Hf-W fractionation model

182Hf-182W evolution in early Solar System

182Hf-182W evolution relative to εW(CHUR)

Continuous Model

1. Solar Nebula2. Mantle

3. Core

Accretion

Fractionation

f iHf /W=

Hf180 / W183 j Hf180 / W183 CHUR

−1

A measure of how separated Hf and W have become

Transport of Stable Species

d i23=ci3C i2

=M 23

M 12

C i2C i1

= 1d i23−11

C i3C i1

=d i23

d i23−11

Transport of Parents

f 2r / s=

d s23−d r23d r23−11

f 3r / s=

−1d s23−d r23d s23d r23−11

f 2r / s=

d s231− f 3

r / s=−1

Since d_r23 = 0, we have:

Transport of Daughter IsotopeFor the specific case of Hf-182 we have that concentrations of daughter products don't vary much over earth's history, and the system is extinct. These give simplifications which lead to the forms:

W CHUR=104 C Hf182 10C W182 10

f 2H /W I , t

I , t =∫0

t

M 2 x M 2t

1 f 2

r /s

e− xdx

d3=−d2f 2r / s

W W isotope model constraintsisotope model constraints

Cores of terrestrial planets

Earth t2stage = 28.1 MyrMoon t2stage = 29.5 MyrMars t2stage = 3.3/9.7 MyrIron meteorites t2stage < 2.8 Myr

Asteroid Vesta

Eucrites ( “easily discerned” ) Vesta’s mantle t2stage = 2.6 Myr